Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28:215001, 2011], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/momentum coordinates. Possible super-luminal phenomena are determined by the width of locally (...) anisotropic brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity. (shrink)

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.

Among the different approaches to questions of biomedical ethics, there is a view that stresses the importance of a patient’s right to make her own decisions in evaluative questions concerning her own well-being. This approach, the autonomy-based approach to biomedical ethics, has usually led to the adoption of a subjective theory of well-being on the basis of its commitment to the value of autonomy and to the view that well-being is always relative to a subject. In this article, it is (...) argued that these two commitments need not lead to subjectivism concerning the nature of well-being. (shrink)

The first part of the paper is a metatheoretical consideration of such philosophy of nature which allows for using scientific results in philosophical analyses. An epistemological 'judgment' of those results becomes a preliminary task of this discipline: this involves taking a position in the controversy between realistic and antirealistic accounts of science. It is shown that a philosopher of nature has to be a realist, if his task to build true ontology of reality is to be achieved. At the same (...) time he cannot be a realist ˗ a possibility that science itself is capable of deciding what beings really exist (a typical realistic claim is that scientific notions refer to something external and truly describe its characteristics) has to be denied, if the philosophy of nature is seen as a discipline investigating the natural world, while being epistemologically different from the natural sciences. A possibility of weakening this opposition is explored in the second part of the paper, where the idea of so-called "postulated ontology" of scientific theories is brought to the consideration. This idea appears in the context of a well-known thesis of the underdetermination of scientific theories by empirical data. It is argued in the paper, that the conviction of the existence of some kind of relation between a given theory and ontological ideas can be derived from this thesis, regardless of its particular form. Therefore, certain solutions to classical philosophical questions can be obtained, in principle, by careful inspection of scientific achievements. However, if the thesis of underdetermination holds, such philosophical solutions are not imposed by science itself. In order to arrive at some kind of ontology based on science, it seems necessary to accept certain philosophical presuppositions in the first place. This and the fact that scientific theories change in time show that although such a kind of ontology is possible, and perhaps desirable, it can never be ultimate. (shrink)

This excellent, semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, and more) and coverage of Einstein’s special and general theories of relativity, discussing the concept of simultaneity, kinematics, Einstein’s mechanics and dynamics, and more.

In my last two books 2012 and 2014, I investigated some important problems of cognitive neuroscience. The general conclusion of these two works (2012 and 2014) is that cognitive neuroscience is a pseudo-science. In Part I of this book 2014, Chapter 1, I introduce the EDWs perspective (from my book published in 2012). In Part II, I investigate more troubles with cognitive neuroscience. (For other troubles of this “science”, see Vacariu 2012, Vacariu and Vacariu 2013) In Chapter 2, I analyze (...) in detail a particular aspect of human visual perception: spatial cognition. In order to be able to offer more arguments on the idea that cognitive neuroscience is a pseudoscience, I need to investigate spatial cognition, an essential feature of visual perception and one of the most important topics of cognitive neuroscience. In Chapter 3, I continue to investigate the most recent successful works in cognitive neuroscience: the Gallant’s laboratory work in relationship with “integration” and “distribution”. In Chapter 4, I analyze the multisensory integration (crossmodal interactions), a more general form of binding problem (a problem that I analyzed in Vacariu 2012). This means that from a particular sensorial system (the classical binding problem), I moved to the multisensorial integration (crossmodal interactions): at least two sensorial mechanisms are involved in creating a perceptual representation. In Chapter 5, I investigate Bechtel’s work on endogenous brain activity (I analyzed his work in my latest books) and, moreover, I update information regarding the default network and the mind-wandering (see also Vacariu 2012). In Chapter 6, I question the relationship between the micro-neuronal level, the macro-neuronal level, oscillations and cognition. An important question needs an answer: “How can we better explain cognition: using knowledge from macro-neuronal level (furnished by fMRI, EEG etc.) or micro-neuronal level or both?” The last application of EDWs perspective is on Einstein’s theory of relativity (Part III of this book 2014) just because this theory is true and it has no problems in explaining certain phenomena and it is completely recognized by specialists in physics. In Appendix, “Did Markus Gabriel (Bonn University) plagiarize my ideas?”, I analyze the UNBELIEVABLE similarities between my ideas from my works (2005, 2008, 2010, 2011, 2012) and Markus Gabriel’s ideas (Bonn University) from his book published in 2013 and his TED clip (also in 2013). (shrink)

When addressing the notion of proper time in the theory of relativity, it is usually taken for granted that the time read by an accelerated clock is given by the Minkowski proper time. However, there are authors like Harvey Brown that consider necessary an extra assumption to arrive at this result, the so-called clock hypothesis. In opposition to Brown, Richard TW Arthur takes the clock hypothesis to be already implicit in the theory. In this paper I will present a (...) view different from these authors by recovering Einstein's notion of natural clock and showing its relevance to the debate. (shrink)

Dennis Dieks advanced the view that the idea of flow of time is implemented in the theory of relativity. The ‘flow’ results from the successive happening/becoming of events along the time-like worldline of a material system. This leads to a view of now as local to each worldline. Each past event of the worldline has occurred once as a nowpoint,and we take there to be an ever-changing present now-point ‘marking’ the unfolding of a physical system. In Dieks’ approach there (...) is no preferred worldline and only along each worldline is there a Newtonian-like linear order between successive now-points. We have a flow of time per worldline. Also there is no global temporal order of the now-points of different worldlines. There is, as much, what Dieks calls a partial order. However Dieks needs for a consistency reason to impose a limitation on the assignment of the now-points along different worldlines. In this work it is made the claim that Dieks’ consistency requirement is, in fact, inbuilt in the theory as a spatial relation between physical systems and processes. Furthermore, in this work we will consider (very) particular cases of assignments of now-points restricted by this spatial relation, in which the now-points taken to be simultaneous are not relative to the adopted inertial reference frame. (shrink)

Summary It is here shown that the relativistic doctrine of the relativity of simultaneity is untenable and that both the special and general theories of relativity are inconsistent. It is also shown that the theories can perhaps be made consistent, but excessively weak, through the reintroduction of absolute space and a weakening of the Lorentz transformations. Non-relativistic hypotheses for some events thought to require relativity are suggested. Finally, some conjectures are made on how so wrong (...) a theory could have been accepted by so many for so long. (shrink)

The considerations of the two former articles concerning the special and general theories of relativity are extended. The question of the physical reality of the ether and the interpretation of some cosmological problems are discussed. A view is expanded according to which the metric tensor g is taken as the energy momentum tensor of the ether. The gravitational equation of Einstein is considered to represent the equations of motion of the ether. The cosmological red shift is also interpreted (...) in such terms. (shrink)

I discuss a rarely mentioned correspondence between Einstein and Swann on the constructive approach to the special theory of relativity, in which Einstein points out that the attempts to construct a dynamical explanation of relativistic kinematical effects require postulating a fundamental length scale in the level of the dynamics. I use this correspondence to shed light on several issues under dispute in current philosophy of spacetime that were highlighted recently in Harvey Brown’s monograph Physical Relativity, namely, Einstein’s view (...) on the distinction between principle and constructive theories, and the consequences of pursuing the constructive approach in the context of spacetime theories. r 2008 Elsevier Ltd. All rights reserved. (shrink)

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic (...) properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. (shrink)

The paper (given in the section on "Recent work in the History of Philosophy of Science) discusses the method and some of the results of the doctoral dissertation on philosophical interpretations of Einstein's special and general theories of relativity, submitted to the Dept. for History of Science, Univ. of Hamburg, in 1989, also published by Birkhauser, Basel, in 1990. It is claimed that many of the gross oversimplifications, misunderstandings and misinterpretations occurring in more than 2500 texts about the (...)theories of relativity written by scientists, philosophers, and laymen contemporary to Einstein can in fact serve as a clue to a better understanding of the general process by which philosophical interpretations are formed. Another very important source for answering the question of how misinterpretations are formed are hitherto unpublished documents in the estates of physicists and philosophers of that time, including apart from Einstein himself: Bergson, Bridgman, Carnap, Cassirer, Metz, Meyerson, Petzoldt, Reichenbach, Schlick and Vaihinger. (shrink)

We want to consider anew the question, which is recurrent along the history of philosophy, of the relationship between rationality and mathematics, by inquiring to which extent the structuration of rationality, which ensures the unity of its function under a variety of forms (and even according to an evolution of these forms), could be considered as homeomorphic with that of mathematical thought, taken in its movement and made concrete in its theories. This idea, which is as old as philosophy (...) itself, although it has not been dominant, has still been present to some degree in the thought of modern science, in Descartes as well as in Kant, Poincaré or Einstein (and a few other scientists and philosophers). It has been often harshly questioned, notably in the contemporaneous period, due to the failure of the logistic programme, as well as to the variety of “empirical” knowledges, and, in a general way, to the character of knowledges that show them as transitory, evolutive and mind-built. However, the analysis of scientific thought through its inventive and creative processes leads to characterize this thought as a type of rational form whose configurations can be detailed rather precisely. In this work we shall propose, first, a quick sketch of some philosophical requirements for such a research programme, among which the need for an harmonization, and even a conciliation, between the notions of rational (or rationality), of intuitive grasp and of creative thought. Then we shall examine some processes of creative scientific thought bearing on the knowledge and the understanding of the world, distinct from mathematics although keeping tight relations with them. Contemporary physical theories are privileged witnesses in this respect, for in them the rational thought of phenomena makes an intrinsic use of mathematical thought, which contributes to the structuration of the formers and to the expression of their concepts (which entails the physical contents of the latter). The General Theory of Relativity and the Quantum Theory are exemplar to this, as they directly reveal what can be called the “drag of physical thought par the mathematical form”, which makes possible to overcome the limitations of the physical knowledge previously adquired. This process is tightly related to the modalities and to the stucture of the rational thought underlying it. This is what we would like to show. DOI:10.5007/1808-1711.2011v15n2p303. (shrink)

Modern readers turning to Einstein’s famous 1905 paper on special relativity may not find what they expect. Its title, “On the electrodynamics of moving bodies,” gives no inkling that it will develop an account of space and time that will topple Newton’s system. Even its first paragraph just calls to mind an elementary experimental result due to Faraday concerning the interaction of a magnet and conductor. Only then does Einstein get down to the business of space and time and (...) lay out a new theory in which rapidly moving rods shrink and clocks slow and the speed of light becomes an impassable barrier. This special theory of relativity has a central place in modern physics. As the first of the modern theories, it provides the foundation for particle physics and for Einstein’s general theory of relativity; and it is the last point of agreement between them. It has also received considerable attention outside physics. It is the first port of call for philosophers and other thinkers, seeking to understand what Einstein did and why it changed everything. It is often also their last port. The theory is arresting enough to demand serious reflection and, unlike quantum theory and general relativity, its essential content can be grasped fully by someone merely with a command of simple algebra. It contains Einstein’s analysis of simultaneity, probably the most celebrated conceptual analysis of the century. (shrink)

The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c in relativistic mechanics cannot be Newtonian mechanics sensu stricto. (...) In this paper I focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics. (shrink)

The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c → ∞ in relativistic mechanics cannot be Newtonian mechanics (...) sensu stricto. In this paper I focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one (...) free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

The present paper is meant to summarise and enlighten the theoretical implications of the twin theories of text comprehension and of text compression. Compatibility and non-exclusiveness of particle-like analysis of language and wave-like analysis of intentionality are also demonstrated within the newly established quantum linguistics framework. The informative state of language is viewed as being relatively stable; once activated and subject to motion, therefore reaching a communicative state, different phenomena occur, which may be observed, analysed and visualised through CPP-TRS (...) observational devices. Relativity theory may therefore be organised in terms of quanta with continuity and no contradiction. (shrink)

Cornea (2012) argues that I (2011) was wrong to use the analogy between morality and motion to defend cultural relativism. I reply that the analogy can be used to clarify what cultural relativism asserts and how a cultural relativist can reply to the criticisms against it. Ockham’s Razor favours the relativist view that there are no moral truths, and hence no culture is better than another. Contrary to what Cornea claims, cultural relativism does not entail that we cannot protect ourselves (...) from those who attack us, and that the ruling of an international court lacks moral legitimacy. (shrink)

In the exuberance that followed Einstein’s discoveries, philosophers at one time or another have proposed that his theories support virtually every conceivable moral in ontology. I present an opinionated assessment, designed to avoid this overabundance. We learn from Einstein’s theories of novel entanglements of categories once held distinct: space with time; space and time with matter; and space and time with causality. We do not learn that all is relative, that time in the fourth dimension in any non-trivial (...) sense, that coordinate systems and even geometry are conventional or that spacetime should be reduced ontologically to causal, spatio-temporal or other relations. (shrink)

The interaction interpretation of special relativity theory (elaborated in Part I) is discussed in relation to quantum theory. The relativistic transformations (Lorentz processes) of physical variables, on the interaction interpretation, are observation-interaction dependent, just as are the physical values (eigenvalues) of systems described by quantum-theoretic state functions; a common, basic structure of the special relativity and quantum theories can therefore be presented. The constancy of the light speed is shown to follow from interaction-transformations of frequency and wavelength (...) variables. A parallelism is suggested between, on the one hand, the Lorentz-Clausius distinction for relativistic transformations, and, on the other, the distinction between observation-dependent and observation-independent natural processes. The empirical study of rates of macroscopic clocks can provide a critical test of the interaction interpretation and of a possible extension to gravitational time changes; the role of time as prior determinant of natural process is at issue. The Hafele-Keating observations are of general relativity effects on clocks in accelerated motion. (shrink)

The present paper develops arguments for the need to formulate the basic theories of physics in terms of a six-dimensional manifold, as opposed to the four-dimensional space-time continuum of conventional theory. Employing a purely classical approach, some of the dynamical consequences of such a formulation with regard to both electrodynamics and gravitation are evaluated. The results lead to interesting implications with regard to various questions such as the occurrence and importance of superluminal particles, the existence of two or more (...) physically distinct time scales, and the variation of the gravitational coupling constant G and the law of energy conservation. The analysis also suggests a physical interpretation of the additional coordinates that occur in the metric. (shrink)

The axiomatic approaches of quantum mechanics and relativity theory are compared with approaches in which the theories are thought to describe readings of certain measurement operations. The usual axioms are shown to correspond with classes of ideal measurements. The necessity is discussed of generalizing the formalisms of both quantum mechanics and relativity theory so as to encompass more realistic nonideal measurements. It is argued that this generalization favours an empiricist interpretation of the mathematical formalisms over a realist (...) one. (shrink)

The axiomatic approaches of quantum mechanics and relativity theory are compared with approaches in which the theories are thought to describe readings of certain measurement operations. The usual axioms are shown to correspond with classes of ideal measurements. The necessity is discussed of generalizing the formalisms of both quantum mechanics and relativity theory so as to encompass more realistic nonideal measurements. It is argued that this generalization favours an empiricist interpretation of the mathematical formalisms over a realist (...) one. (shrink)

In this paper I argue that the debate between subjective and objective theories of prudential value obscures the way in which elements of both are needed for a comprehensive theory of prudential value. I suggest that we characterize these two types of theory in terms of their different aims: procedural (or subjective) theories give an account of the necessary conditions for something to count as good for a person, while substantive (or objective) theories give an account of (...) what is good for a person, given some set of necessary conditions. Characterizing the theories in this way allows us to see their mutual compatibility. To make this case, I assume that a theory of prudential value ought to be descriptively and normatively adequate. The criterion of descriptive adequacy requires that our theory explain the subject relativity of prudential value. I characterize subject relativity in terms of justifiability to subjects and I argue that certain procedural theories are well suited to meet this criterion. The criterion of normative adequacy requires that our theory be capable of guiding action and I argue that a certain kind of substantive theory is needed to meet this requirement. (shrink)

Peter Kosso (2013) discusses the weak gravitational lensing observations of the Bullet Cluster and argues that dark matter can be detected in this system solely through the equivalence principle without the need to specify a full theory of gravity. This paper argues that Kosso gets some of the details wrong in his analysis of the implications of the Bullet Cluster observations for the Dark Matter Double Bind and the possibility of constructing robust tests of theories of gravity at galactic (...) and greater scales. Even the Bullet Cluster evidence is not sufficiently detailed to allow precision tests of General Relativity that would distinguish it from its rivals at galactic and greater scales. Taking into account the total evidence available, we cannot rule out "ugly" solutions to the dynamical discrepancy in astrophysics that involve both a large quantity of dark matter and a theory of gravity whose predictions differ significantly from those of General Relativity for interactions taking place at galactic and greater scales. (C) 2014 Elsevier Ltd. All rights reserved. (shrink)

That space and time should be integrated into a single entity, spacetime, is the great insight of Einstein's special theory of relativity, and leads us to regard spacetime as a fundamental context in which to make sense of the world around us. But it is not the only one. Causality is equally important and at least as far as the special theory goes, it cannot be subsumed under a fundamentally geometrical form of explanation. In fact, the agent of propagation (...) of causal influence is electromagnetic radiation. In this examination, the authors find support for a rationalist approach to physics, never neglecting experimentation, but rejecting a simple empiricist or positivist view of science. (shrink)

It is said that the theory of relativity and quantum theory are independent of each other. Their relationship is like water and oil. Now, it is very important for modern physics to synthesize them. In Physics and mathematics, Super String theory is studied, but instead of it, the tendimensional world appears. Our world is a three-dimensional world . What is the ten-dimensional world? It is more difficult than the string which is of Plank length. In the ten dimensional world, (...) physics is facing darkness and nothingness which man can not explain with the traditional physical words.The solution depends upon philosophy. I tried to synthesize themand succeeded.The following is an outline of my synthesis. 1. Utility and relativity of mathematical truth Mathematical truth is not absolute but relative. In the universe ( outside the solar system ), there is no perfect line. Because, by the gravitation of large astronomical bodies, space and lines are curved. Mathematical figure and numeration depend upon the promise of mankind. These are not absolute. Physics, which is grounded upon mathematics in certainty, is also relative. It expresses not the whole of the universe but a part of the universe. 2. Community and difference between the theory of relativity and quantum theory Community is the negation of absoluteness of physical attributes. Difference is the assessment for mathematics. The theory of relativity relies on mathematics but quantumtheory does not always rely on it. According to circumstances, Niels Bohr and quantum physicists abandoned a frame of reference. 3. The origin of the theory of relativity 4. The origin of quantum theory In short, the theory of relativity and quantum theory are not perfect, they only irradiate a part of the universe. Man can reach the whole of the universe only by the philosophical intuition of nothingness and infinite (the principle of nothingness and love). (shrink)

A procedure is given for the transformation of quantum mechanical operator equations into stochastic equations. The stochastic equations reveal a simple correlation between quantum mechanics and classical mechanics: Quantum mechanics operates with “optimal estimations,” classical mechanics is the limit of “complete information.” In this connection, Schrödinger's substitution relationsp x → -iħ ∂/∂x, etc, reveal themselves as exact mathematical transformation formulas. The stochastic version of quantum mechanical equations provides an explanation for the difficulties in correlating quantum mechanics and the theory of (...)relativity: In physics “time” is always thought of as a numerical parameter; but in the present formalism of physics “time” is described by two formally totally different quantities. One of these two “times” is a numerical parameter and the other a random variable. This last concept of time shows all the properties required by the theory of relativity and is therefore to be considered as the relativistic time. (shrink)

Inertial frames and Lorentz transformations have a preferred status in the special theory of relativity (STR). Lorentz transformations, in turn, embody Einstein's convention that the velocity of light is isotropic, a convention that is necessary for the establishment of a standard signal synchrony. If the preferred status of Lorentz transformations in STR is not due to some particular bias introduced by a convention on signal synchronism, but to the fact that the Lorentz transformation group is the symmetry group of (...) the theory, then the signal synchronism is not a matter of convention but rather a matter of fact. In order to explore the conventionalist thesis, that within the frame of STR isotropy in the velocity of light and, hence, signal synchronism is a matter of convention, we need a generalized Lorentz transformation group that does not embody Einstein's isotropy convention, and upon which STR can be based. We present here a new approach to the resulting search for a generalized STR, which is well suited for establishing some well-known results of Winnie as well as some new results. (shrink)

The considerations of Part I are extended and the experimental data and hypotheses that led to the establishment of the general theory of relativity are analyzed. It is found that one of the fundamental assumptions is that light is propagated homogeneously; i.e., by using arbitrary systems of coordinates, propagation of light can be represented by a homogeneous quadratic form. This is shown to be an assumption that can be verified by experiment, at least in principle. As a result of (...) adding a number of further assumptions to this, the usual formalism of the general theory of relativity can be established. In the above point of view, the general theory of relativity—like any other theory—cannot be built upad hoc, but is built on distinct physical hypotheses, each of which can be subjected to test by experiment. (shrink)

The purpose of the present paper is to reply to a misleading paper by M. Sachs entitled “Einstein's later view of the Twin Paradox” (TP) (Found. Phys. 15, 977 (1985)). There, by selecting some passages from Einstein's papers, he tried to convince the reader that Einstein changed his mind regarding the asymmetric aging of the twins on different motions. Also Sachs insinuates that he presented several years ago “convincing mathematical arguments” proving that the theory of relativity does not predict (...) asymmetrical aging in the TP. Here we give a definitive treatment to the clocks problem showing that Sachs' “convincing mathematical arguments” are non sequitur. Also, by properly quoting Einstein, we show that his later view of the TP coincides with the one derived from the rigorous theory of time developed in this paper. (shrink)